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Roadmap on methods and software for electronic structure based simulations in chemistry and materials

This Roadmap article provides a succinct, comprehensive overview of the state of electronic structure methods and software for molecular and materials simulations. Seventeen distinct sections collect insights by 51 leading scientists in the field. Each contribution addresses the status of a particular area, as well as current challenges and anticipated future advances, with a particular eye towards software related aspects and providing key references for further reading. Foundational sections cover density functional theory and its implementation in real-world simulation frameworks, Green's function based many-body perturbation theory, wave-function based and stochastic electronic structure approaches, relativistic effects and semiempirical electronic structure theory approaches. Subsequent sections cover nuclear quantum effects, real-time propagation of the electronic structure, challenges for computational spectroscopy simulations, and exploration of complex potential energy surfaces. The final sections summarize practical aspects, including computational workflows for complex simulation tasks, the impact of current and future high-performance computing architectures, software engineering practices, education and training to maintain and broaden the community, as well as the status of and needs for electronic structure based modeling from the vantage point of industry environments. Overall, the field of electronic structure software and method development continues to unlock immense opportunities for future scientific discovery, based on the growing ability of computations to reveal complex phenomena, processes and properties that are determined by the make-up of matter at the atomic scale, with high precision.

36 MATERIALS SCIENCE↗

Single-crystalline orthorhombic GdAlGe as a rare-earth magnetic Dirac nodal-line metal

Crystal engineering is a method for discovering new quantum materials and phases, which may be achieved using external pressure or strain. Chemical pressure is unique in that it generates internal pressure perpetually to the lattice. As an example, GdAlSi from the rare-earth (𝑅) 𝑅⁢Al⁢𝑋 (𝑋=Si or Ge) family of Weyl semimetals is considered. Replacing Si with the larger isovalent element Ge creates sufficiently large chemical pressure to induce a structural transition from the tetragonal structure of GdAlSi, compatible with a Weyl semimetallic state, to an orthorhombic phase in GdAlGe, resulting in an inversion-symmetry-protected nodal-line metal. We find that GdAlGe hosts an antiferromagnetic ground state with two successive orderings, at 𝑇 N ⁢1=35K and 𝑇 N ⁢2=30K. In-plane isothermal magnetization shows a magnetic field induced metamagnetic transition at 6.2 T for 2 K. Furthermore, electron-hole compensation gives rise to a large magnetoresistance of ∼100% at 2 K and 14 T. Angle-resolved photoemission spectroscopy measurements and density functional theory calculations reveal a Dirac-like linear band dispersion over an exceptionally large energy range of ∼1.5eV with a high Fermi velocity of ∼10 6 m/s, a rare feature not observed in any magnetic topological materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Layer-dependent spin-resolved electronic structure of ferromagnetic triple-layered ruthenate Sr4Ru3O10

High-resolution angle- and spin-resolved photoemission spectroscopy (ARPES) of the triple-layered ruthenate Sr4Ru3O10 reveals features of the electronic structure that extend our understanding of the layered strontium ruthenates. The spectra near the Fermi energy are very different from the nonmagnetic analogues Sr2RuO4 and Sr3Ru2O7 with distinct Fermi surfaces for wide electronlike minority spin bands around the zone center and narrow holelike majority spin Fermi surface contours around the zone corners. The most dramatic results are two narrow spectral peaks ∼30 meV below the Fermi level, a spin-minority holelike band at the Brillouin zone center, and a spin-majority saddle-band van Hove singularity at the zone edge, which exhibits almost 100% spin polarization at low temperature, and a strong temperature dependent coherence-incoherence crossover attributed to Hund metal correlations. Quantitative comparison of the ARPES to spin-polarized density functional theory (DFT) calculations identify the specific antibonding and nonbonding orbital origins of the narrow bands, with a prediction of different spatial localization in the central and outer layers. This is shown to be consistent with experimental ARPES multizone matrix element intensity variations, and implicates outer-layer-specific control of the in-plane metamagnetism. The renormalization of the bands relative to the mean-field DFT, the demonstration of spin-polarized oxygen bands, and of spin-minority and spin-majority band-crossing hybridization provide a more complete picture of the magnetism which displays aspects of both delocalized and local moment behavior.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Range-separated thermal hybrid exchange-correlation density functional for accurate band-gap calculations of warm dense matter

Here, in this study, we present a range-separated thermal hybrid exchange-correlation (XC) functional, termed RS-KDT0, which provides highly accurate band-gap predictions at elevated temperature while reducing the computational cost relative to thermal global hybrid functionals. At zero temperature, RS-KDT0 recovers the widely used ground-state range-separated hybrid functional HSE06. To assess its performance across temperature regimes, we conducted static calculations of electronic pressure, band gaps, and band structures. RS-KDT0 exhibits the same level of accuracy as HSE06 in the low-temperature regime and demonstrates improved agreement with finite-temperature GW calculations at elevated temperatures when compared to other thermal XC functionals such as the generalized gradient approximation (GGA)-level KDT16 and the global hybrid KDT0.

density functional theory↗

Crystal Growth of Quaternary Rare Earth Selenosilicates by Using the Flux-Assisted Boron Chalcogen Mixture Method: Investigation of Their Magnetic and Optical Properties

A series of rare earth magnesium selenosilicates, RE3Mg 0.5 SiSe 7 (RE = Ce, Pr, Nd, Sm, Gd, Tb, Dy) were obtained as single crystal using the flux assisted boron chalcogen mixture (BCM) method. The structures of the crystals were determined by single-crystal X-ray diffraction. The RE3Mg 0.5 SiSe 7 series crystallizes in the hexagonal crystal system in the space group P6 3 . Polycrystalline powders were synthesized to perform physical property measurements. Magnetic measurements over the 2–300 K temperature range reveal that Ce 3 Mg 0.5 SiSe 7 and Gd 3 Mg 0.5 SiSe 7 exhibit paramagnetic behavior with negative Weiss constants (θ W = −14.50, θ W = −6.13 K, respectively). The optical properties of RE 3 Mg 0.5 SiSe 7 (RE = Ce, Pr, Nd, Sm, Gd) were measured by ultraviolet–visible (UV–vis) diffuse reflectance. Density functional theory (DFT) electronic structure calculations were performed. Furthermore, a second harmonic generation measurement was performed on a polycrystalline powder of Ce 3 Mg 0.5 SiSe 7 and was found to be SHG active with an efficiency of 0.11 times the standard potassium dihydrogen phosphate (KDP).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The electronic structure, crystal fields, and magnetic anisotropy in RECo 5 magnets

The current progress in describing rare-earth-based magnets' electronic structure and magnetic properties is discussed. We use several currently popular electronic structure methods to show the typical values of critical parameters that define the physics of RECo 5 (RE = rare earth atom) materials. The magnetic moments and magnetic anisotropy of 4f atoms are obtained using several approaches, including anisotropic 4f-charge density-constrained DFT and DFT+HI methods. We also suggest the introduction of "penalty" functional for obtaining correct variational total energy in the traditional Hund's rule-constrained DFT-based techniques. The applicability and future extensions are discussed. The proposed combination of methods is potentially suitable for high-throughput computational searches of new rare-earth-containing magnetic materials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The Electron Thermal Conductivity of Pu and Zr Substituted Gamma-Uranium

Uranium alloys are attractive recycled nuclear fuels because of their high thermal conductivity (k) and fissile density; however, the effects of alloying elements on k remain unclear. Here, the electron thermal conductivity (k_e) of U-Pu-Zr compositions are calculated using density functional theory. The electronic structure is evaluated to understand the effects of plutonium (Pu) and zirconium (Zr) substitution on the k_e of ?-U. Alloys of up to 37.5 at. % Pu and 37.5 at. % Zr are examined. Two methods are applied to calculate k_e; we find that the accuracy of each method depends on the electronic and mass similarities between the solute and solvent atoms. Specifically, when the solute atom is similar in electronic structure and mass, the method that applies the electron relaxation time of ?-U is best, while if the elements are dissimilar, a mixed method that mixes several parameters associated with k_e from each element in the alloy is best. The introduction of all alloying elements decreases k_e; however, in binary compounds, Pu and Zr have different effects. Pu generally flattens the electronic bands but compensates for this deleterious effect by increasing electron density near the Fermi level. Zr flattens the electronic bands more severely without adding electron density near the Fermi level. Therefore, Zr decreases the k_e more than Pu in binary compounds. In ternary compounds, the difference between Pu and Zr is minimal due to the phononic change from the large mass change of Zr substitution, even at 12.5 at. %. Thus, we predict that higher loadings of Pu, and potentially other actinides, can be added to U-Pu-Zr compositions for faster recycling of spent fuel with without sacrificing k. We also note that these k_e calculation methods can be applied to non-fuel alloys that require k_e predictions, such as cladding, heat exchanger, and structural materials.

36 MATERIALS SCIENCE↗

The Electron Thermal Conductivity of Pu and Zr Substituted $\mathcal{γ}$-U

Uranium alloys are attractive recycled nuclear fuels because of their high thermal conductivity (𝑘) and fissile density. Limited experimental studies of the 𝑘 of U-Pu-Zr alloys in the range of 15 to 20 wt% Pu and 6 to 15 wt% Zr indicate that increasing the content of either Zr or Pu tends to lower 𝑘. However, which element has the greater effect on 𝑘, and the associated mechanisms, remains unclear. Here, in this study, the electron thermal conductivity (𝑘 𝑒 ) of U-Pu-Zr compositions are calculated using density functional theory. The electronic structure is evaluated to understand the effects of plutonium (Pu) and zirconium (Zr) substitution on the 𝑘 𝑒 of 𝛾-U. Alloys of up to 37.5 at. % Pu and 37.5 at. % Zr are examined. Two methods are applied to calculate 𝑘 𝑒 ; we find that the accuracy of each method depends on the electronic and mass similarities between the solute and solvent atoms. Specifically, when the solute atom is similar in electronic structure and mass, the more accurate method is that which employs the electron relaxation time of 𝛾-U, while if the elements are dissimilar, a mixed method that mixes several parameters associated with JNW_S⁢3033426825100132 from each element in the alloy is best. The introduction of all alloying elements decreases 𝑘 𝑒 ; however, in binary compounds, Pu and Zr have different effects. Pu flattens the electronic bands but compensates for this deleterious effect by increasing electron density near the Fermi level. Zr flattens the electronic bands more severely without adding electron density near the Fermi level. Therefore, Zr decreases 𝑘 𝑒 more than Pu in binary compounds. In ternary compounds, the difference between Pu and Zr is minimal due to the phononic change from the large mass change of Zr substitution, even at 12.5 at. %. Thus, we predict that higher loadings of Pu, and potentially other actinides, can be added to U-Pu-Zr compositions for faster recycling of spent fuel without sacrificing 𝑘. We also note that these 𝑘 𝑒 calculation methods can be applied to non-fuel alloys that require 𝑘 𝑒 predictions, such as cladding, heat exchanger, and structural materials.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Fragme∩t: An Open‐Source Framework for Multiscale Quantum Chemistry Based on Fragmentation

Fragment-based quantum chemistry offers a means to circumvent the nonlinear computational scaling of conventional electronic structure calculations, by partitioning a large calculation into smaller subsystems then considering the many-body interactions between them. Variants of this approach have been used to parameterize classical force fields and machine learning potentials, applications that benefit from interoperability between quantum chemistry codes. However, there is a dearth of software that provides interoperability yet is purpose-built to handle the combinatorial complexity of fragment-based calculations. To fill this void we introduce “Fragme∩t”, an open-source software application that provides a tool for community validation of fragment-based methods, a platform for developing new approximations, and a framework for analyzing many-body interactions. Fragme∩t includes algorithms for automatic fragment generation and structure modification, and for distance- and energy-based screening of the requisite subsystems. Checkpointing, database management, and parallelization are handled internally and results are archived in a portable database. Interfaces to various quantum chemistry engines are easy to write and exist already for Q-Chem, PySCF, xTB, Orca, CP2K, MRCC, Psi4, NWChem, GAMESS, and MOPAC. Applications reported here demonstrate parallel efficiencies around 96% on more than 1000 processors but also showcase that the code can handle large-scale protein fragmentation using only workstation hardware, all with a codebase that is designed to be usable by non-experts. Fragme∩t conforms to modern software engineering best practices and is built upon well established technologies including Python, SQLite, and Ray. The source code is available under the Apache 2.0 license.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Solid-State Hydroxide Ion Conductivity in Silver(I) Oxide, Ag 2 O

Silver (I) oxide, Ag 2 O, precipitated as microcrystals by combining aqueous silver(I) nitrate and KOH solutions, was found to be a solid-state hydroxide ion conductor with ionic conductivity on the order of 10 -3 S/cm. The proton chemical shifts at 4.87 and -7.35 ppm measured by solid-state 1H-NMR experiments are attributed to water molecules and in-lattice OH - coordinated to silver, respectively. The lack of spinning sidebands around the 4.87 ppm peak indicates rapid reorientation on the NMR timescale, suggesting that the water molecules are adsorbed to the surface of the Ag 2 O crystals. Pulsed field gradient measurements gave similar diffusion coefficients (2 x 10 -7 cm 2 /s at 298K) for all three proton environments indicating chemical exchange between sites on the millisecond timescale. The activation energy for OH - diffusion measured by NMR (0.18 eV) was comparable to that obtained by conductivity measurements and density functional theory (DFT) electronic structure calculations. Furthermore, the calculated Pourbaix diagram of Ag 2 O is consistent with the slightly lower sample density observed in He pycnometry and thermogravimetric measurements.

25 ENERGY STORAGE↗

Taming the virtual space for incremental full configuration interaction

Incremental full configuration interaction (iFCI) closely approximates the FCI limit with polynomial cost through a many-body expansion of the correlation energy, providing highly accurate total energies within a given basis set. To extend iFCI beyond previous basis set limitations, this work introduces a novel natural orbital (NO) screening approach, incremental NO full configuration interaction (iNO-FCI). By consideration of the importance of virtual orbital selection in the convergence of iFCI, iNO-FCI maximizes the consistency between orbitals selected for each correlated body. iNO-FCI employs a principle of cancellation of errors and ensures that the same set of virtual NOs is used for interdependent terms. Here, this strategy significantly reduces computational cost without compromising precision. Computational savings of up to 95% are demonstrated, allowing access to larger basis sets that were previously computationally prohibitive. iNO-FCI is herein introduced and benchmarked for several difficult test cases involving double-bond dissociation, biradical systems, conjugated π systems, and the spin gap of a Cu-based transition metal complex.

Correlation energy↗

First-principles computations of the Stark shift of a defect-bound exciton: The case of the T center in silicon

The T center in silicon has recently drawn a lot of attention for its potential in quantum information science. The sensitivity of the zero-phonon line (ZPL) to electrical field was recently investigated by a combination of different experimental methods but there are still few first principles studies on the Stark shift of the T center. Dealing with the defect-bound exciton nature of the excited state is particularly challenging using density functional theory because of the large spatial delocalization associated with the wavefunction. Here, in this work, we tackle this issue by performing a convergence study over the supercell size. We obtain an exciton binding energy of 28.5 meV, in good agreement with experimental results. We then calculate the Stark shift through the dipole moment change of the ZPL transition of the T center using the modern theory of polarization formalism and find a modest linear coefficient of Δ⁢𝜇=0.79⁢D along X and Δ⁢𝜇=0.03⁢𝐷 along Y. We discuss our results in light of the recent experimental measurements of the Stark shift. Our analysis suggests that bound-exciton defects could be particularly sensitive to local field effect as a result of their large spatial extent.

color centers↗

Pauli potential formalism at finite temperature

At zero temperature, the Pauli potential—the functional derivative of the Pauli kinetic energy density functional—is the key to the accuracy of the orbital-free density functional theory (OFDFT) as it is supposed to capture all the effects associated with the Pauli exclusion principle. Here, we extend this concept to finite temperature by defining Pauli free energy and the modified Pauli free energy, both representing the natural generalizations of the Pauli term from zero- T to finite- T . We discuss their physical interpretation, the mathematical nuances, and the applicability, arguing that the modified Pauli potential should be used as an extension of the zero- T counterpart within the OF-DFT framework. Through analytical and numerical methods, we then analyze some of the exact properties concerning the modified Pauli free- and kinetic-energy terms and examine the temperature dependence of the modified Pauli potential.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Spin-Dependent $\pi$$\pi$* Gap in Graphene on a Magnetic Substrate

Here, we present a detailed analysis of the electronic properties of graphene/Eu/Ni(111). By using angle- and spin-resolved photoemission spectroscopy and ab initio calculations, we show that the intercalation of Eu in the graphene/Ni(111) interface gives rise to a gapped freestanding dispersion of the $\pi$$\pi$* Dirac cones at the K point with an additional lifting of the spin degeneracy due to the mixing of graphene and Eu states. The interaction with the magnetic substrate results in a large spin-dependent gap in the Dirac cones with a topological nature characterized by a large Berry curvature and a spin-polarized Van Hove singularity, whose closeness to the Fermi level gives rise to a polaronic band.

36 MATERIALS SCIENCE↗

Controlling 4 f antiferromagnetic dynamics via itinerant electronic susceptibility

Optical manipulation of magnetism holds promise for future ultrafast spintronics, especially with lanthanides and their huge, localized 4 f magnetic moments. These moments interact indirectly by spin polarizing the conduction electrons (the Ruderman-Kittel-Kasuya-Yosida exchange interaction), influenced by interatomic orbital overlap, and the conduction electron's susceptibility around the Fermi level. Here, we study this influence in a series of 4 f antiferromagnets, Gd T 2 Si 2 ( T = Co, Rh, Ir), using ultrafast resonant x-ray diffraction. We observe a twofold increase in the ultrafast intersublattice angular momentum transfer rate between the materials, originating from modifications in the conduction electron susceptibility, as confirmed by first-principles calculations. Published by the American Physical Society 2024

36 MATERIALS SCIENCE↗

Putting error bars on density functional theory dataset

This dataset contains submission files and raw output files from high-throughput DFT simulations to analyze the systemic errors in lattice constant, bulk moduli and formation energy predictions for a range of binary and ternary oxides using four exchange correlation functionals (LDA, PBE, PBEsol and vdW-DF-C09). This data was then used as the basis for employing materials informatics methods to predict the expected errors in the lattice constants of the studied compounds. Predicted errors were also used to better the DFT-predicted lattice parameters. Our results emphasize the link between the computed errors and the electron density and hybridization errors of a functional. In essence, these results provide “error bars” for choosing a functional for the creation of high-accuracy, high-throughput datasets as well as avenues for the development of XC functionals with enhanced performance, thereby enabling the accelerated discovery and design of new materials.

36 MATERIALS SCIENCE↗

HydraGNN_Predictive_GFM_2024 - Ensemble of predictive graph foundation models for ground state atomistic materials modeling

We provide the ensemble of fifteen pre-trained graph foundation models (GFMs) for atomistic materials modeling applications. Each one of the fifteen GFMs has been trained on five open-source datasets that (once aggregated) amount to over 154 million atomistic structures, which cover over two-thirds of the natural elements of the periodic table and that comprises a broad set of organic and inorganic compounds. This vast set of atomistic structures comprises ground state configurations that are dynamically stable (i.e., equilibrated structures with atomic forces approximately close to zero values) as well as dynamically unstable structures (i.e., non-equilibrium structures with non-negligible non-zero values of atomic forces). The ensemble of datasets aggregated does NOT include excited states. The datasets have been curated to remove atomistic structures with spectral norm of the force tensor above 100 eV/angstrom. Moreover, a linear term of the energy was computed for each dataset using a linear regression model that uses the chemical concentration of each natural element as regressor. The linear term predicted by the linear regression model has been subtracted from each original energy value to perform a re-alignment of the energy values across different electronic structures approximation theories performed to generate the diverse multi-source, multi-fidelity datasets. The folder "ADIOS_files" contains the set of pre-processed datasets in Adaptable I/O System (ADIOS) format (https://www.exascaleproject.org/research-project/adios/) that have been used for the development and training of GFMs in this work. The "ADIOS_files" directory contains 6 sub-directories named as follows: - ANI1x-v3.bp - MPTrj-v3.bp - OC2020-20M-v3.bp - OC2020-v3.bp - OC2022-v3.bp - qm7x-v3.bp Each sub-directory contains the pre-processed datasets converted in Adaptable I/O System (ADIOS) format (https://www.exascaleproject.org/research-project/adios/) that have been used to the development, training, and performance testing of the ensemble go predictive graph foundation models. Each GFM was developed using HydraGNN (https://github.com/ORNL/HydraGNN) as underlying graph neural network (GNN) architecture. The multi-task learning (MTL) capability of HydraGNN was used to simultaneously train the GFMs on labeled values for direct predictions of energy (a total system property of an atomistic structure that measures the chemical stability) and atomic forces (an atomic level property of an atomistic structure that measures the dynamical stability). The hyper parameters of the GFM have been tuned using scalable hyperparameter optimization (HPO) algorithms implemented in the software DeepHyper (https://github.com/deephyper/deephyper). The pre-training of each HPO trial was performed using distributed data parallelism (DDP) to scale the training across 128 compute nodes of the exascale OLCF supercomputer Frontier. Each HPO trial was trained only for 10 epochs and an early stopping was performed to avoid wasting significant computational resources on GNN architectures that were clearly underperforming. For each HPO trial, the 'omnistat' tool developed by (AMD Research - Advanced Micro Device) was used to measure the total energy consumption in kWh. The ensemble of GFMs was obtained by selecting the fifteen best performing HPO trials. Four models have been selected for their clear advantage in accuracy, and these are the GFMs with IDs 229, 156, 147, 260. Additional eleven models have been selected based on judicious balance between accuracy and energy consumption needed for training, and these are the GFMs with IDs 165, 78, 137, 1, 175, 171, 181, 67, 179, 167, 351. Each selected GFM of the ensemble was continued to cumulate a total of at most 30 epochs. In some cases, the total number of epochs actually performed was les than 30 due to two combined factors: (1) the size of the GFM (i.e., the number of model parameters to train) and (2) the total wall-clock time for which the computational resources could be allocated on OLCF-Frontier. The "Ensemble_of_models" directory contains 15 sub-directories named as follows: - gfm_0.229 - gfm_0.156 - gfm_0.147 - gfm_0.260 - gfm_0.165 - gfm_0.78 - gfm_0.137 - gfm_0.1 - gfm_0.175 - gfm_0.171 - gfm_0.181 - gfm_0.67 - gfm_0.179 - gfm_0.167 - gfm_0.351 Each one of these sub-directories refers to one of the fifteen HPO trials that have been selected to continue the pre-training with at most 30 epochs. With each sub-directory associated with a specific HPO trial, the following files can be found: - config.json: file for argument parsing to develop and train an HydraGNN architecture - gfm_0.ID_epoch_N.pk: file with model parameters for HPO ID trial after N epochs of training The ensemble of fifteen GFM architectures was used for (1) ensemble averaging to stabilize the predictions of energy and atomic forces after pre-training for post-processing analysis and (2) ensemble uncertainty quantification (UQ). The code used to develop, pre-train, and load the pre-trained models for post-processing analysis is available on the ORNL-GitHub at the following link: https://github.com/ORNL/HydraGNN/tree/Predictive_GFM_2024

36 MATERIALS SCIENCE↗

Toward improved property prediction of 2D materials using many-body quantum Monte Carlo methods

The field of 2D materials has grown dramatically in the past two decades. 2D materials can be utilized for a variety of next-generation optoelectronic, spintronic, clean energy, and quantum computing applications. These 2D structures, which are often exfoliated from layered van der Waals materials, possess highly inhomogeneous electron densities and can possess short- and long-range electron correlations. The complexities of 2D materials make them challenging to study with standard mean-field electronic structure methods such as density functional theory (DFT), which relies on approximations for the unknown exchange-correlation functional. To overcome the limitations of DFT, highly accurate many-body electronic structure approaches such as diffusion Monte Carlo (DMC) can be utilized. In the past decade, DMC has been used to calculate accurate magnetic, electronic, excitonic, and topological properties in addition to accurately capturing interlayer interactions and cohesion and adsorption energetics of 2D materials. Here, this approach has been applied to 2D systems of wide interest, including graphene, phosphorene, MoS 2 , CrI 3 , VSe 2 , GaSe, GeSe, borophene, and several others. In this review article, we highlight some successful recent applications of DMC to 2D systems for improved property predictions beyond standard DFT.

2D materials↗